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Economic interpretation of fractional derivatives

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  • Valentina V. Tarasova
  • Vasily E. Tarasov

Abstract

An economic interpretation of the Caputo derivatives of non-integer orders is proposed. The suggested economic interpretation of the fractional derivatives is based on a generalization of average and marginal values of economic indicators. We formulate an economic interpretation by using the concept of the T-indicator that allows us to describe economic processes with memory. The standard average and marginal values of indicator are special cases of the proposed T-indicator, when the order is equal to zero and one, respectively. The fractional derivatives are interpreted as economic characteristics (indicators) that are intermediate between the standard average and marginal values of indicators.

Suggested Citation

  • Valentina V. Tarasova & Vasily E. Tarasov, 2017. "Economic interpretation of fractional derivatives," Papers 1712.09575, arXiv.org.
    • Handle: RePEc:arx:papers:1712.09575
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    File URL: http://arxiv.org/pdf/1712.09575
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    References listed on IDEAS

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    1. מחקר - ביטוח לאומי, 1996. "Volume 4," Working Papers 65, National Insurance Institute of Israel.
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    Citations

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    Cited by:

    1. Valentina V. Tarasova & Vasily E. Tarasov, 2016. "Fractional Dynamics of Natural Growth and Memory Effect in Economics," Papers 1612.09060, arXiv.org, revised Jan 2017.
    2. Tarasova, Valentina V. & Tarasov, Vasily E., 2017. "Logistic map with memory from economic model," Chaos, Solitons & Fractals, Elsevier, vol. 95(C), pages 84-91.
    3. Valentina V. Tarasova & Vasily E. Tarasov, 2017. "Dynamic intersectoral models with power-law memory," Papers 1712.09087, arXiv.org.
    4. Tarasov, Vasily E. & Tarasova, Valentina V., 2018. "Macroeconomic models with long dynamic memory: Fractional calculus approach," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 466-486.
    5. Asifa, & Kumam, Poom & Tassaddiq, Asifa & Watthayu, Wiboonsak & Shah, Zahir & Anwar, Talha, 2022. "Modeling and simulation based investigation of unsteady MHD radiative flow of rate type fluid; a comparative fractional analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 486-507.
    6. Jajarmi, Amin & Hajipour, Mojtaba & Baleanu, Dumitru, 2017. "New aspects of the adaptive synchronization and hyperchaos suppression of a financial model," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 285-296.
    7. Vasily E. Tarasov, 2019. "Rules for Fractional-Dynamic Generalizations: Difficulties of Constructing Fractional Dynamic Models," Mathematics, MDPI, vol. 7(6), pages 1-50, June.
    8. Vasily E. Tarasov, 2023. "General Fractional Calculus in Multi-Dimensional Space: Riesz Form," Mathematics, MDPI, vol. 11(7), pages 1-20, March.
    9. Aslan Lotfi & Zhengrui Jiang & Ali Lotfi & Dipak C. Jain, 2023. "Estimating Life Cycle Sales of Technology Products with Frequent Repeat Purchases: A Fractional Calculus-Based Approach," Information Systems Research, INFORMS, vol. 34(2), pages 409-422, June.
    10. Vasily E. Tarasov, 2019. "On History of Mathematical Economics: Application of Fractional Calculus," Mathematics, MDPI, vol. 7(6), pages 1-28, June.
    11. Inés Tejado & Emiliano Pérez & Duarte Valério, 2020. "Fractional Derivatives for Economic Growth Modelling of the Group of Twenty: Application to Prediction," Mathematics, MDPI, vol. 8(1), pages 1-21, January.
    12. Jiong Weng & Xiaojing Liu & Youhe Zhou & Jizeng Wang, 2022. "An Explicit Wavelet Method for Solution of Nonlinear Fractional Wave Equations," Mathematics, MDPI, vol. 10(21), pages 1-14, October.
    13. Murat A. Sultanov & Durdimurod K. Durdiev & Askar A. Rahmonov, 2021. "Construction of an Explicit Solution of a Time-Fractional Multidimensional Differential Equation," Mathematics, MDPI, vol. 9(17), pages 1-12, August.
    14. Shi, Jianping & He, Ke & Fang, Hui, 2022. "Chaos, Hopf bifurcation and control of a fractional-order delay financial system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 348-364.
    15. Riaz, M.B. & Iftikhar, N., 2020. "A comparative study of heat transfer analysis of MHD Maxwell fluid in view of local and nonlocal differential operators," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    16. Hajipour, Ahamad & Hajipour, Mojtaba & Baleanu, Dumitru, 2018. "On the adaptive sliding mode controller for a hyperchaotic fractional-order financial system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 497(C), pages 139-153.
    17. Valentina V. Tarasova & Vasily E. Tarasov, 2017. "Concept of dynamic memory in economics," Papers 1712.09088, arXiv.org.
    18. Valentina V. Tarasova & Vasily E. Tarasov, 2016. "Economic Accelerator with Memory: Discrete Time Approach," Papers 1612.07913, arXiv.org, revised Jul 2017.
    19. Valentina V. Tarasova & Vasily E. Tarasov, 2017. "Logistic map with memory from economic model," Papers 1712.09092, arXiv.org.

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